In recent years, in an internal combustion engine mounted on a vehicle, a target air-fuel ratio of emission gas is set to the vicinity of the stoichiometric air-fuel ratio which is the highest cleaning performance range of a catalyst of a three-way catalyst or the like, and an air-fuel ratio is controlled by a feedback control such that an air-fuel ratio of emission gas detected by an air-fuel ratio sensor becomes the target air-fuel ratio to thereby promote an emission gas cleaning efficiency of the catalyst.
Further, according to a vehicle in recent years, fuel cut-off for stopping fuel injection in deceleration operation or the like is carried out to improve fuel cost. During the fuel cut-off, intake air is discharged from an engine into an exhaust pipe without being subjected to combustion. Therefore, oxygen in uncombusted emission gas is brought into a state of being adsorbed in the catalyst by a large amount. Therefore, after finishing the fuel cut-off, even when an air-fuel ratio of emission gas is controlled by a feedback control to the vicinity of the stoichiometric air-fuel ratio which is an ordinary target air-fuel ratio, a cleaning function inherent to the catalyst cannot be achieved by the large amount of oxygen adsorbed in the catalyst during the fuel cut-off.
Hence, according to a vehicle in recent years, after finishing the fuel cut-off, the target air-fuel ratio is shifted temporarily in a direction richer than the stoichiometric air-duel ratio and rich control for controlling the air-fuel ratio of emission gas to be richer than the stoichiometric air-fuel ratio is carried out to thereby make the oxygen adsorbed in the catalyst react with HC in emission gas to be removed to recover the cleaning function which the catalyst possesses.
Generally, the output characteristic of an air-fuel ratio sensor has a characteristic that although an air-fuel ratio can be detected with high accuracy when an error (tolerance) with respect to a standard output characteristic becomes substantially null at the vicinity of the stoichiometric air-fuel ratio (excess air ratio λ=1), the more remote from the stoichiometric air-fuel ratio, the more enlarged the detection error with respect to the standard output characteristic to thereby deteriorate detection accuracy. Therefore, in the above rich control after finishing the fuel cut-off, even when the air-fuel ratio of emission gas is controlled by a feedback control to a target air-fuel ratio λtg richer than the stoichiometric air-fuel ratio, since the detection accuracy of the air-fuel ratio sensor is poor in the rich air-fuel region, the air-fuel ratio of emission gas cannot be controlled accurately to the target air-fuel ratio λtg in the rich control. As a result, the actual air-fuel ratio λr of emission gas is shifted to a side richer than the target air-fuel ratio λtg in the rich control, an emission amount of a component rich in CO, HC or the like is increased, or, the actual air-fuel ratio λr for emission gas is shifted to a side leaner than the target air-fuel ratio λtg in the rich control to thereby increase an emission amount of NOx.
For compensating for an error in an output of an air-fuel ratio sensor, in for example U.S. Pat. No. 5,778,866 (JP-A-9-203343), a change characteristic (inclination characteristic) of an output of an air-fuel ratio sensor is learned until elapse of a predetermined time period from start of fuel cut-off, the change characteristic is compared with a previously determined reference change characteristic (inclination characteristic) to form correction data and the output of the air-fuel ratio sensor is corrected by the correction data.
However although according to the sensor output correcting method, the change characteristic of the air-fuel ratio sensor is learned after starting the fuel cut-off, the change characteristic of the output of the air-fuel ratio sensor is changed also by a factor other than the error of the output of the air-fuel ratio sensor (for example, an emission gas flow rate, a state of adsorbing a lean/rich component or a degree of deterioration thereof at start of the fuel cut-off, or the like). Therefore, even when the change characteristic of the output of the air-fuel ratio sensor is measured after starting the fuel cut-off, the error of the output of the air-fuel ratio sensor cannot accurately be learned and correction accuracy of the output of the air-fuel ratio sensor is poor.
Further, in U.S. Pat. No. 4,546,747 (JP-2503381), an actual limit current of an air-fuel ratio sensor is detected in a specific operating state (for example, a steady-state operating state at low or middle load), a deviation between the actual limit current (detected air-fuel ratio) and a target limit current (target air-fuel ratio) previously stored in correspondence with the specific operating state is calculated, a correction coefficient is calculated based on the deviation and the output of the air-fuel ratio sensor is corrected by the correction coefficient.
However, although according to the sensor output correcting method, the correction coefficient is calculated based on the deviation between the actual limit current (detected air-fuel ratio) of the air-fuel ratio sensor and the previously stored target limit current (target air-fuel ratio) in the specific operating state, during the feedback control of the air-fuel ratio, the feedback control is carried out such that the actual limit current (detected air-fuel ratio) of the air-fuel ratio sensor coincides with the target limit current (target air-fuel ratio). Therefore, the deviation between the actual limit current (detected air-fuel ratio) of the air-fuel ratio sensor and the target limit current (target air-fuel ratio) is reduced, the error of the output of the air-fuel ratio sensor cannot accurately be learned and the correction accuracy of the output of the air-fuel ratio sensor is still poor.